[physics.soc-ph] The origin of life poses a problem of combinatorial feasibility: How can temporally supported functional organization arise in exponentially branching assembly spaces when unguided exploration behaves as a memoryless random walk?
We show that nonlinear threshold-cascade dynamics in connected interaction networks provide a minimal, substrate-agnostic mechanism that can soften this obstruction. Below a critical connectivity threshold, cascades die out locally and structured input-output response mappings remain sparse and transient-a “functional desert” in which accumulation is dynamically unsupported.
Near the critical percolation threshold, system-spanning cascades emerge, enabling discriminative functional responses. We illustrate this transition using a minimal toy model and generalize the argument to arbitrary networked systems.
Also near criticality, cascades introduce finite-timescale structural and functional coherence, directional bias, and weak dynamical path-dependence into otherwise memoryless exploration, allowing biased accumulation.
This connectivity-driven transition-functional percolation-requires only generic ingredients: interacting units, nonlinear thresholds, influence transmission, and non-zero coherence times.
The mechanism does not explain specific biochemical pathways, but it identifies a necessary dynamical regime in which structured functional organization can emerge and be temporarily supported, providing a physical foundation for how combinatorial feasibility barriers can be crossed through network dynamics alone.
Galen J. Wilkerson
Comments: 11 pages, 2 figures
Subjects: Physics and Society (physics.soc-ph); Adaptation and Self-Organizing Systems (nlin.AO); Biological Physics (physics.bio-ph); Molecular Networks (q-bio.MN); Populations and Evolution (q-bio.PE)
MSC classes: 37N25
ACM classes: J.3; J.2; G.2.2; G.3; I.6.5; F.2.2
Cite as: arXiv:2601.06272 [physics.soc-ph] (or arXiv:2601.06272v3 [physics.soc-ph] for this version)
https://doi.org/10.48550/arXiv.2601.06272
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Submission history
From: Galen Wilkerson
[v1] Fri, 9 Jan 2026 19:37:36 UTC (45 KB)
[v2] Wed, 21 Jan 2026 00:01:31 UTC (47 KB)
[v3] Sat, 24 Jan 2026 19:50:52 UTC (28 KB)
https://arxiv.org/abs/2601.06272
Astrobiology, Origin of Life,
